package DP;

/**
 * @Author: Gosin
 * @Date: 2020/5/25 18:38
 * 最短路径和的问题
 */
public class MinPathSum {
    public static void main(String[] args) {
        int[][] grid = {
            {1,2,5},
            {3,2,1}
        };
        MinPathSum sum = new MinPathSum();
        int i = sum.minPathSum(grid);
        System.out.println(i);
    }
    public int minPathSum(int[][] grid) {
        //最优子结构的问题
        //状态数组先定义一个二维的数组
        //dp方程
        //f(i,j) = Min(f(i,j-1),f(i-1,j))+grid(i,j)
        if(grid.length<=0){return 0;}
        int[][] dp = new int[grid.length][grid[0].length];
        dp[0][0]=grid[0][0];
        for(int i=1;i<grid.length;i++){
            dp[i][0] = dp[i-1][0]+grid[i][0];
        }
        for(int i=1;i<grid[0].length;i++){
            dp[0][i] = dp[0][i-1]+grid[0][i];
        }
        for(int i =1;i<grid.length;i++){
            for(int j=1;j<grid[0].length;j++){
                dp[i][j] = Math.min(dp[i-1][j],dp[i][j-1])+grid[i][j];
            }
        }
        return dp[grid.length-1][grid[0].length-1];
    }
}
